Why is my UV mapped texture dissapearing when I start blender game engine
I have downloaded and test the file which you have attached.
Pressing P does reveal the image in the game engine on my screen.

I suspect you user preferences setting were different from mine.

Now that I see your graphics card, I am suspecting it could be a hardware/software limitation. I went on the internet and search for OpenGL driver for the card. And it seems that you have to download a package to enable OpenGL support. Maybe you could read up here and download the appropriate OpenGL package for your card?

Link here https://downloadcenter.intel.com/download/20046/OpenGL-Support-Web-Link

Link to the G41 Express Chipset here https://downloadcenter.intel.com/product/81517/Graphics-Drivers-for-Intel-G41-Express-Chipset

Hope this will resolve your issue, good luck.